Matrix Equations and Structures: Efficient Solution of Special Discrete Algebraic Riccati Equations
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
On the sensitivity of noncoherent capacity to the channel model
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Capacity bounds for peak-constrained multiantenna wideband channels
IEEE Transactions on Communications
Noncoherent capacity of underspread fading channels
IEEE Transactions on Information Theory
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We study the asymptotic behavior of the eigenvalues of Hermitian n × n block Toeplitz matrices Tn, with k × k blocks, as n tends to infinity. No hypothesis is made concerning the structure of the blocks. Such matrices {Tn} are generated by the Fourier coefficients of a Hermitian matrix-valued function $f\in L^2$, and we study the distribution of their eigenvalues for large n, relating their behavior to some properties of f as a function; in particular, we show that the distribution of the eigenvalues converges to a limit $\mu_f$, and we explicitly compute $\mu_f$ in terms of f, showing that $\int F\, d\mu_f=1/k\int\tr F(f)$. Some consequences of this distribution and some localization results for the eigenvalues of Tn are discussed. We also study the eigenvalues of the preconditioned matrices {Pn-1Tn}, where the sequence {Pn} is generated by a positive definite matrix-valued function p. We show that the spectrum of any Pn-1Tn is contained in the interval [r,R], where r is the smallest and R the largest eigenvalue of p-1f. We also prove that the first m eigenvalues of Pn-1Tn tend to r and the last m tend to R, for any fixed m. Finally, the exact limit value of the condition number of the preconditioned matrices is computed.